This invention relates to a synchronous motor control system for controlling a synchronous motor in such a manner that the torque thereof is held constant. More particularly, the invention relates to a synchronous motor control system capable of reducing a follow-up delay in the current flowing through each of the windings of the synchronous motor.
Servomotors are employed widely in a variety of fields, and even AC servomotors have been developed in recent years. Synchronous motors also can be utilized as servomotors. In particular, since synchronous motors which use a permanent magnet as the rotor, are of the brushless type, they are simple in construction and do not generate noise. For these reasons, such synchronous motors are coming into ever wider use. In a synchronous motor of this kind, it is necessary that torque be controlled so as to be constant. To this end, there has been developed a technique in which control is exercised in such a manner that a current of the same phase as an electromotive force induced by the rotor is caused to flow into the windings of the armature, which serves as the stator. This technique will now be described using the drawing of FIG. 1, which shows the construction of a synchronous motor. The magnetic flux density B at a position displaced by .theta. degrees from the q axis of the magnetic field generated by a rotor 1, namely a permanent magnet, is given by the following: EQU B=B.sub.m sin .theta. (1)
The magnetic flux .phi. interlinked with the a winding of a stator 2 shown in FIG. 1 is expressed as follows: EQU .phi.=-.phi..sub.m cos .theta..sub.c ( 2)
where .phi..sub.m represents the magnetic flux on the q axis of the rotor 1.
Accordingly, the electromotive force e.sub.1 induced in the a winding is expressed as follows: ##EQU1## (where .theta.=P.theta.m=P.multidot..omega..sub.m .multidot.t).
Likewise, the electromotive forces e.sub.2, e.sub.3 induced in the b and c windings of the stator 2, which are disposed at angles of 1/3.pi. and 2/3.pi. relative to the a winding, respectively, are expressed by the following: ##EQU2##
If we let the currents flowing in the armature windings a, b, c be i.sub.1, i.sub.2, i.sub.3, respectively, then the output torque T of such a three-phase synchronous motor will be expressed by the following: EQU T1/2(e.sub.1 .multidot.i.sub.1 +e.sub.2 .multidot.i.sub.2 +e.sub.3 .multidot.i.sub.3) (6)
Therefore, substituting Eqs. (3), (4) and (5) into Eq. (6), we have: ##EQU3## To render the torque T constant, it should be so arranged that T is independent of the angle .theta.. Therefore, if the following relations hold, namely: ##EQU4## where I is the current amplitude, then the torque T of Eq. (7) may be written as follows: ##EQU5## Thus, the torque T is constant, being independent of the rotational orientation of the rotor 1.
To carry out such control, it is necessary to detect the rotor angle of the synchronous motor and regulate each of the armature current values in accordance therewith.
However, if the current flowing through each armature winding is delayed by .phi..sub.o from the ideal value, then the currents i.sub.1, i.sub.2, i.sub.3 of the respective armature windings will take on the form: ##EQU6## In consequence, the output torque T will be take on the form: ##EQU7## Thus, the torque will decrease in value.
In the control circuit of a synchronous motor, the gain of a current control loop is finite and cannot be made infinitely large. A delay in response is, therefore, inevitable. Consequently, even though a rotary encoder for sensing the rotational angle of the synchronous motor may produce an output which is an accurate indication of the rotational angle, the current in the armature winding is delayed from the ideal value. The delay, which is proportional to velocity, becomes large in magnitude.